Optical demodulation allows high-optical-bandwidth LADAR data to be collected with a low-bandwidth electronic camera, using a linear-chirp Frequency Modulated Continuous Wave (“FMCW”) architecture. In this method, each pixel of a detector array (e.g., a camera) is illuminated with a local oscillator (“LO”) beam, as well as with scattered light from a spot on the target scene. Both sources of light carry the same linear (optical) frequency chirp, but in general arrive with different delays at each pixel because of the different path length through the LO leg vs. the round trip to the particular point at the target scene corresponding to that pixel. As a consequence of this time difference and the linear frequency chirp, a heterodyne signal is formed at each pixel that depends on the difference in delay between the two paths, more difference leading to a higher heterodyne frequency (in the absence of acousto-optic frequency shifters, etc.). A different pixel might be imaging a more distant point on the target, and so produce a different heterodyne signal frequency than another pixel viewing a closer point in the target scene. A Fourier transform of each pixel's time series, acquired during the chirp, therefore, affords a range-density estimate for that pixel. Effectively, a time-series of images taken of the target during the chirp is stacked, and a Fourier transform is performed through the stack. Aliasing can be avoided if the frame rate is high enough to capture at least two images per cycle of the highest heterodyne signal present.
This imaging scheme is ambiguous in range-Doppler, however, as target motion results in Doppler-shifted returns that cannot be distinguished from returns from a different range. The Doppler sensitivity is very high, with a slight radial target velocity sufficient to change range of just λ/2 (e.g., ˜1 micron) during the chirp placing the estimated target range in the next range bin (e.g., 1-100 cm). The range-Doppler ambiguity arising from uniform motion, however, can be measured by taking data during both up-chirps and down-chirps, which have different ambiguity functions, and it can be compensated for by shifting the LO optical frequency by one or more acousto-optic modulators (“AOMs”) in either or both of the LO or target light paths. In this way, the highly-shifted return coming from a rapidly, but constantly, moving target can nevertheless be made to produce a low heterodyne frequency compatible with alias-free measurement using low camera frame rates.
Different situations arise, however, if the target moves non-uniformly. If the Doppler shift is not constant, it can't be removed with a simple frequency offset. Ultimately, if the target motion is irregular, and/or the target itself is flexible, the foregoing methods break down, and can provide no useful range information.